It's energy that's being stored rather than power - power is a measure of the rate of energy release. 1 Watt is 1 Joule per Second. In fact battery capacities are written as the amount of charge they hold (mAh or Ah) to give an idea of how long they will last for a given current draw. Putting batteries in parallel will not increase the current (for the same load) as the voltage is the same , but the the same current can be drawn for longer as the capacity is bigger.